Revisiting anisotropy in the tensile and fracture behavior ......Heterogeneous nano-lamellar...

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Revisiting anisotropy in the tensile and fracture behavior of cold-rolled 316L stainless steel with heterogeneous nano-lamellar structures Zesheng You a, * , Huangliu Fu a , Shoudao Qu a , Weikang Bao a , Lei Lu b, ** a Herbert Gleiter Institute of Nanoscience, Nanjing University of Science and Technology, Nanjing, 210094, China b Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang, 110016, China ARTICLE INFO Keywords: Heterogeneous nano-lamellar structure Mechanical anisotropy Fracture behavior Specimen size effect Strain path effect ABSTRACT We produced a 316L stainless steel with heterogeneous nanometer-thick lamellar structures by severe cold-rolling at room temperature, and conducted micro-scale tensile tests in different orientations to evaluate both the in- plane (parallel to the nano-lamellae) and out-of-plane (normal and 45 inclined to the nano-lamellae) mechan- ical anisotropy. The parallel orientation demonstrates the greatest tensile strength while the inclined orientation exhibits the least strength. The tensile tests in normal and inclined directions also indicate signicant transient elastic-plastic response due to the strain path change. Fractographic examination demonstrates that the specimen fails in the normal direction by premature micro-void nucleation and growth, which restricts its tensile strength; however, we identied zig-zag cracking associated with lamellar shear cracking in the inclined direction. 1. Introduction Nano-lamellar single-phase metals and multi-phase composites have received considerable attention recently owing to their appealing me- chanical properties, such as high strength, enhanced thermal stability, promoted fatigue resistance and radiation damage tolerance [15]. The nano-lamellar structures can be generated by monotonic severe plastic deformation, such as high pressure torsion (HPT) [6], accumulative roll bonding (ARB) [7,8], cold rolling [9,10] and surface mechanical grinding [1,11], or alternatively by bottom-up techniques, including electro-deposition and magnetron sputtering [12,13]. The preferential alignment of the internal grain boundaries or phase interfaces unavoid- ably leads to signicant anisotropy in various material properties. For example, the strengthening effect may substantially vary depending on the loading direction with respect to the lamellae [14,15]. Thus, it is important to perform systematic mechanical investigations in different stressing directions to quantify the magnitude of the plastic anisotropy and to determine the ways in which the underlying deformation mech- anism depends on the loading direction. However, constrained by nite specimen thicknesses, most mechan- ical evaluations currently available have been conducted parallel to the lamellar structures [1618]. The out-of-plane mechanical measurements are rather scarce. Recently, this deciency has been remedied practically by a rapid development in micro-mechanical evaluation techniques based on nano-indentations and micro-pillar compressions [1921]. However, regarding the micro mechanical investigations, there are some ambiguities which must be claried. First, the strengths from the microscale tests is not only related to the microstructural feature, but also constitutes a complicated function of the indenter or specimen size [22, 23]. Second, although nano-indentation and micro compressions are advantageous for measuring strength, information on ductility and strain hardening is not directly accessible by such tests. Moreover, compressive stress suppresses the potential failure related to the laminated structures. Tensile tests must be conducted uniaxially in different directions to achieve a better understanding of the effect of lamellar directionality on the inherent tensile ductility and fracture behavior. Previous researchers have conducted a series of tension experiments to investigate the mechanical behavior of cold-rolled 316L stainless steel (SS) consisting of nano-scale lamellar structures parallel to rolling plane [2427]. Miura et al. have reported a signicant in-plane mechanical anisotropy with strength in transverse direction much higher than in rolling direction [26]. However, there is still a lack of the out-of-plane mechanical tests necessary to determine the strength and tensile ductility when the nano-lamellae are normal or highly inclined to the stressing direction. In this study, we have carefully explored the tensile behaviors perpendicular, parallel, and 45 inclined to the lamellar * Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (Z. You), [email protected] (L. Lu). Contents lists available at ScienceDirect Nano Materials Science journal homepage: www.keaipublishing.com/cn/journals/nano-materials-science/ https://doi.org/10.1016/j.nanoms.2020.03.001 Available online 11 March 2020 2589-9651/© 2020 Chongqing University. Production and hosting by Elsevier B.V. on behalf of KeAi. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Nano Materials Science 2 (2020) 7279

Transcript of Revisiting anisotropy in the tensile and fracture behavior ......Heterogeneous nano-lamellar...

  • Nano Materials Science 2 (2020) 72–79

    Contents lists available at ScienceDirect

    Nano Materials Science

    journal homepage: www.keaipublishing.com/cn/journals/nano-materials-science/

    Revisiting anisotropy in the tensile and fracture behavior of cold-rolled316L stainless steel with heterogeneous nano-lamellar structures

    Zesheng You a,*, Huangliu Fu a, Shoudao Qu a, Weikang Bao a, Lei Lu b,**

    a Herbert Gleiter Institute of Nanoscience, Nanjing University of Science and Technology, Nanjing, 210094, Chinab Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang, 110016, China

    A R T I C L E I N F O

    Keywords:Heterogeneous nano-lamellar structureMechanical anisotropyFracture behaviorSpecimen size effectStrain path effect

    * Corresponding author.** Corresponding author.

    E-mail addresses: [email protected] (Z. You), l

    https://doi.org/10.1016/j.nanoms.2020.03.001

    Available online 11 March 20202589-9651/© 2020 Chongqing University. Product(http://creativecommons.org/licenses/by-nc-nd/4.0/).

    A B S T R A C T

    We produced a 316L stainless steel with heterogeneous nanometer-thick lamellar structures by severe cold-rollingat room temperature, and conducted micro-scale tensile tests in different orientations to evaluate both the in-plane (parallel to the nano-lamellae) and out-of-plane (normal and 45� inclined to the nano-lamellae) mechan-ical anisotropy. The parallel orientation demonstrates the greatest tensile strength while the inclined orientationexhibits the least strength. The tensile tests in normal and inclined directions also indicate significant transientelastic-plastic response due to the strain path change. Fractographic examination demonstrates that the specimenfails in the normal direction by premature micro-void nucleation and growth, which restricts its tensile strength;however, we identified zig-zag cracking associated with lamellar shear cracking in the inclined direction.

    1. Introduction

    Nano-lamellar single-phase metals and multi-phase composites havereceived considerable attention recently owing to their appealing me-chanical properties, such as high strength, enhanced thermal stability,promoted fatigue resistance and radiation damage tolerance [1–5]. Thenano-lamellar structures can be generated by monotonic severe plasticdeformation, such as high pressure torsion (HPT) [6], accumulative rollbonding (ARB) [7,8], cold rolling [9,10] and surfacemechanical grinding[1,11], or alternatively by bottom-up techniques, includingelectro-deposition and magnetron sputtering [12,13]. The preferentialalignment of the internal grain boundaries or phase interfaces unavoid-ably leads to significant anisotropy in various material properties. Forexample, the strengthening effect may substantially vary depending onthe loading direction with respect to the lamellae [14,15]. Thus, it isimportant to perform systematic mechanical investigations in differentstressing directions to quantify the magnitude of the plastic anisotropyand to determine the ways in which the underlying deformation mech-anism depends on the loading direction.

    However, constrained by finite specimen thicknesses, most mechan-ical evaluations currently available have been conducted parallel to thelamellar structures [16–18]. The out-of-plane mechanical measurementsare rather scarce. Recently, this deficiency has been remedied practically

    [email protected] (L. Lu).

    ion and hosting by Elsevier B.V. o

    by a rapid development in micro-mechanical evaluation techniquesbased on nano-indentations and micro-pillar compressions [19–21].However, regarding the micro mechanical investigations, there are someambiguities which must be clarified. First, the strengths from themicroscale tests is not only related to the microstructural feature, but alsoconstitutes a complicated function of the indenter or specimen size [22,23]. Second, although nano-indentation and micro compressions areadvantageous for measuring strength, information on ductility and strainhardening is not directly accessible by such tests. Moreover, compressivestress suppresses the potential failure related to the laminated structures.Tensile tests must be conducted uniaxially in different directions toachieve a better understanding of the effect of lamellar directionality onthe inherent tensile ductility and fracture behavior.

    Previous researchers have conducted a series of tension experimentsto investigate the mechanical behavior of cold-rolled 316L stainless steel(SS) consisting of nano-scale lamellar structures parallel to rolling plane[24–27]. Miura et al. have reported a significant in-plane mechanicalanisotropy with strength in transverse direction much higher than inrolling direction [26]. However, there is still a lack of the out-of-planemechanical tests necessary to determine the strength and tensileductility when the nano-lamellae are normal or highly inclined to thestressing direction. In this study, we have carefully explored the tensilebehaviors perpendicular, parallel, and 45� inclined to the lamellar

    n behalf of KeAi. This is an open access article under the CC BY-NC-ND license

    mailto:[email protected]:[email protected]://crossmark.crossref.org/dialog/?doi=10.1016/j.nanoms.2020.03.001&domain=pdfwww.sciencedirect.com/science/journal/25899651www.keaipublishing.com/cn/journals/nano-materials-science/https://doi.org/10.1016/j.nanoms.2020.03.001http://creativecommons.org/licenses/by-nc-nd/4.0/https://doi.org/10.1016/j.nanoms.2020.03.001https://doi.org/10.1016/j.nanoms.2020.03.001

  • Z. You et al. Nano Materials Science 2 (2020) 72–79

    structure, using micro specimens of over 50 μm thick and sufficientlylarge to eliminate the potential sample size effect We will also probe viafractographic examination the effect of loading direction on the tensilefracture process.

    2. Experimental details

    Thematerial under investigation was a commercial ANSI 316L SS hot-rolled and thermally annealed to obtain equiaxed austenitic grains. Thechemical composition of the material is given in Table 1. The materialwas deformed by cold rolling at room temperature to a final thickness of~4 mm and a total thickness reduction of about 85%, corresponding toan effective true strain of ~2.2.

    We conducted microscale tensile tests in different directions withrespect to the rolling plane to probe the orientation dependence of themechanical response of the cold-rolled sample. As schematically shownin Fig. 1a, we tested two in-plane directions, i.e., the rolling direction(RD) and the transverse direction (TD), as well as two out-of-plane di-rections, i.e., the normal direction (ND) and an inclined direction (ID).The ID was in the TD-ND plane and made an angle of 45� with the TD(Fig. 1a). The micro-tensile specimens were fabricated by a laboratoryfemtosecond laser micromachining system (FemtoLAB, Altechna,Lithuania). Due to the ultra-short pulse duration (~250 fs) of the laserbeam, the material was removed before the heat energy was dissipatedinto surrounding material, thereby producing a negligible heat affectedzone [28–31]. Cross-sectional slices with a thickness of ~500 μm werecut by electrical discharge machining, mechanically ground with suc-cessively finer SiC papers and then electrochemically polished to thetarget thickness (~50 μm) necessary for machining the dog-bone shape.The fabricated micro-specimens were further slightly electro-chemicallypolished to remove fabrication debris and any roughness of the cuttingsurface. Fig. 1b shows an optical micrograph of a high-quality micro--tensile specimen fabricated by this procedure. The specimen had a gaugewidth of 100 μm, a gauge length of 250 μm and a fillet radius of 50 μm.

    The micro tensile tests were conducted on a custom-designed micro-mechanical testing instrument at room temperature. Before the tests, themicro tensile specimen was fixed to a sample holder using ethyl cyano-acrylate glue and carefully moved into a tungsten gripper via a two-axismotorized motion stage, as shown in Fig. 1c. The installation andalignment was monitored in both front and side views by two high res-olution cameras. A piezo stepper linear actuator (N-381 NEXACT, PhysikInstrumente) with a position resolution of 20 nm was used to load thespecimen. The applied force was measured by a miniature tension/compression load cell (LCFD-1KG, Omega Engineering) with a capacityof 10 N and a resolution of about 15 mN. The strain in the gauge sectionwas determined by digital image correlation (DIC) [32,33]. For thispurpose, random black dots were sprayed onto the specimen surface byatomizing black ink, and several subsets of pixels were selected at bothends of the gauge section to calculate the extension, as shown in Fig. 1c.The tensile tests were displacement controlled with a displacement rateof 0.1 μm, corresponding to a nominal strain rate of 3 � 10�4 s�1. Foreach direction, five specimens were tested in order to guarantee thereproducibility of the result.

    For comparison, the tensile tests in the RD and TD were also con-ducted with macro specimens with a gauge length of 5 mm, a gaugesection of 2 � 1 mm2 (a proportional scale-up of the micro specimens).The macro tensile tests were performed on an Instron 5982 mechanicaltesting machine at room temperature with the same strain rate as themicro tensile tests. The gauge strain was also measured by a non-contactDIC strain gauge, as described in detail in Ref. [33].

    Table 1Chemical composition (wt%) of the 316L SS.

    C Mn Si P S Cr Ni Mo Fe

    0.022 1.29 0.37 0.04 0.055 16.64 11.09 2.0 Balance

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    The microstructure of the as-rolled 316L SS was characterized by anFEI Verios 460 field emission gun scanning electron microscope (FEG-SEM) and an FEI TECNAI G2 20 transmission electron microscope (TEM)operating at an accelerating voltage of 200 kV. The fracture surfaces wereexamined by an FEI Quanta 250 FEG-SEM. The phase composition wasanalyzed by X-ray diffraction (XRD) on a Bruker AXS D8 Advancediffractometer with Cu Kα radiation.

    3. Results

    3.1. Microstructure

    Fig. 2 displays the cross-sectional microstructure of the cold rolled316L SS inspected along the TD. The overall SEM micrograph in Fig. 2ademonstrates that the microstructure after severe cold rolling is ratherheterogeneous. Magnified TEM observations (Fig. 2c) reveal that mostregions are occupied by extremely elongated grains forming typicallamellae separated by planar boundaries which are either parallel to ordeviate by small angles from the RD. The boundaries curve with a highdensity of accumulated dislocations. Statistical analysis indicates that thelamellar thickness λ ranges from 10 to 160 nm with a volume averagedvalue of 60 nm (Fig. 2d). Due to the low stacking fault energy of the 316LSS, both the dislocation behavior and deformation twinning act to controlthe rolling deformation and microstructural refinement. It is believedthat twinning is the primary deformation mechanismwhich produces thenano-lamellae (λ < 100 nm) whereas the wide lamellae arise from anaccumulation of dislocations and rotation of subdivided crystallites[34–36]. Deformation twinning takes place only in grains of favorableorientations, and the twins are gradually destructured by localized shearbands (Fig. 2b) to highly elongated grains that are progressively rotatedtowards the rolling plane with increasing rolling strain. Some bundles ofdeformation nanotwins, rhomboid in shape, remain within the lamellarstructures, as shown in Fig. 2a and magnified in Fig. 2b. As roughlyestimated, the nanotwin regions possess a volume fraction of 10–15%,fewer than that (~25%) in the 316L SS treated by dynamic plasticdeformation due to the lower strain rate and larger applied strain [37].TEM observations in Fig. 2e show many dislocations stored along thetwin boundaries (TBs). The twin/matrix lamellar thickness is smallerthan 100 nm, with a volume averaged value of about 30 nm. The XRDprofile in Fig. 2f shows that, in addition to the major γ austenite phase,there are small peaks which belong to α’martensite phase, suggesting theoccurrence of martensite transformation during cold rolling, as oftenidentified for the 316L SS [38,39]. The volume fraction of the martensitephase is estimated to be about 15%.

    3.2. Tensile properties

    Fig. 3 shows the engineering stress–strain curves for the cold-rolled316L SS tested using micro tensile specimens in four different di-rections. We plotted all the curves from the repeated tests for each di-rection on one graph to demonstrate the high reproducibility of the tests,and included representative curves (solid black line without symbols)obtained from the macro tensile tests in the RD and TD for comparison.Table 2 summarizes the derived mechanical properties, including 0.2%offset yield strength (σy), ultimate tensile strength (σuts), uniform elon-gation (δu), and fracture elongation (δf). Fig. 3a shows that the stress–-strain curves from the micro tensile tests are consistent with those fromthe macro tensile tests in the RD. The micro tensions in the TD (Fig. 3b)also exhibit only slightly higher (

  • Fig. 1. (a) Schematic of the micro tensile specimensand their orientations in the cold-rolled plate; (b)micro tensile specimen prepared by femtosecond lasermachining and electrochemically polishing (numbersindicate the dimensions in micrometers); (c) capturedimage showing a micro tensile specimen installed inthe tungsten gripper. The random black dots in (c)were sprayed intentionally; two groups of pixel sub-sets were manually selected at both ends of the gaugesection to measure strain.

    Fig. 2. Cross-sectional microstructure ofcold-rolled 316L SS inspected along TD. (a)Overall SEM observations showing themicrostructural heterogeneity; (b) bundlesof deformation nanotwins cut by localizedshear bands (indicated by arrows); (c) TEMmicrograph showing the lamellar structurewith extended boundaries almost parallel toRD; (d) histogram of lamellar thickness forthe lamellar structures; (e) TEM micrographof a deformation nanotwin bundle (inset isthe selected area diffraction pattern); (f)XRD profile showing the presence of major γaustenite phase and minor α’ martensitephase.

    Z. You et al. Nano Materials Science 2 (2020) 72–79

    findings of previous investigators [26]. The σy value dramatically de-creases to 961 � 52 MPa for θ ¼ 45� (ID), and to 931 � 36 MPa forθ ¼ 90� (ND). The σuts value (1218 � 29 MPa) with θ ¼ 45� is also muchsmaller than those at θ ¼ 0� (RD and TD) but increases again to1409 � 21 MPa for θ ¼ 90� (ND).

    The uniform elongation, δu, is around 2% for tensions in the RD andTD, characteristic of severely deformed metals. Fig. 4b demonstrates thatδu increases slightly to �4% for θ > 45�, whereas the post-neckingelongation δpn¼ δf – δu decreases linearly with increasing θ. This suggeststhat the post-necking tensile behavior is more greatly orientation

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    dependent. After the initiation of necking, the stress decreases slightly ina stable manner until a –δpn of 16% and 11% is achieved in the RD andTD, respectively. In the ID, there is no immediate decrease in stress afternecking initiation, followed by a fast stress reduction and eventualfracture (Fig. 3d) with a δpn of 8.6%, but in the ND the stress is reducedrapidly after necking and δpn is lowered to ~5% (Fig. 3c).

    3.3. Fractographic examination

    Fig. 5 shows the fracture surfaces of the macro specimens in the RD

  • Fig. 3. Engineering stress – strain curves for the micro-tensile tests in (a) RD, (b) TD, (c) ND, (d) ID. The black solid lines without symbols in (a) and (b) are results forthe macro-tensile tests.

    Table 2Tensile properties of the cold-rolled 316L stainless steel tested in different directions. σy, 0.2% offset yield strength; σuts, ultimate tensile strength; δu, uniform elon-gation; δf, fracture elongation; δpn, post-necking elongation.

    Direction Specimen σy (MPa) σuts (MPa) δu (%) δf (%) δpn (%)

    RD Macro 1287 � 54 1439 � 37 2.1 � 0.1 16.2 � 1.1 14.2 � 1.0RD Micro 1311 � 39 1437 � 34 1.7 � 0.1 17.3 � 0.8 15.6 � 0.8TD Macro 1340 � 11 1587 � 14 2.3 � 0.1 12.9 � 0.7 10.6 � 0.8TD Micro 1482 � 55 1701 � 50 2.1 � 0.2 13.0 � 2.5 11.0 � 2.4ND Micro 931 � 36 1409 � 21 3.9 � 0.2 9.0 � 1.1 5.1 � 1.2ID Micro 961 � 52 1218 � 29 4.2 � 0.8 12.9 � 4.0 8.6 � 3.7

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    and TD. In the specimen centers, there are evident delamination fracturesparallel to the lamellar structures in both tensile directions. The delam-ination cracks in the RD (Fig. 5b) are much deeper than those in the TD(Fig. 5d). This suggests that the delamination fracture develops morereadily in the RD, probably a direct consequence of greater microstruc-tural alignment for the RD than for the TD. There are also numerous finedimples arising between these large delamination cracks from the finalabrupt rupture.

    Fig. 6 displays the overall fracture surfaces of the micro tensilespecimens tested in directions different from the lamellar structures.Fig. 6 indicates that the tensile direction significantly impacts the failuremode. The RD and TD tensions, parallel to the lamellar structure, exhibitsimilar failure in a shear mode along an inclined plane after substantialdiffuse necking (Fig. 6a and b). Magnified examinations on the fracturesurface (Fig. 7a and b) reveal that there are only extremely fine andshallow dimples on the smooth fracture planes. The delamination frac-ture, as observed in the macro specimens (Fig. 5), does not take placewhen the specimen size is reduced to the microscale. When tensileloading is perpendicular to the lamellar structure (ND), the necking be-comes much more localized (Fig. 6c). Fig. 7c shows that the fracturesurface becomes rather undulated and that there are numerous ductiledimples of various sizes. Although the fine dimples are generated by the

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    final fracture, the coarse and deep ones probably form early then grow insize during the tensile deformation. For ID, in which tensile direction isinclined to the lamellar structure, the specimen clearly fractured in a zig-zag manner (Figs. 6d and 7d). The zig-zag morphology evidently de-velops via nucleating shear fracture cracks along two different lamellarboundaries, which then interconnect by trans-lamellar shearing inanother direction.

    4. Discussion

    4.1. Specimen size effect

    It is well known that the flow strength of a material is stronglydependent on the specimen size and geometry [40–42]. In particular,the tendency that “smaller is stronger” has often been seen in specimensof size less than 10 μm [23,42,43], which usually causes ambiguityregarding whether the mechanical properties obtained via micro-scaletests are representative of those of the bulk materials. However, wefound that our micro-mechanical experiments produce tensile proper-ties that are specimen size independent compared with those from thecorresponding macro tensile tests. The stress�strain curves of the microand macro tensile tests in the RD entirely coincide, indicating that not

  • Fig. 4. Variations of the mechanical properties of cold-rolled 316L SS as afunction of the angle between the tensile direction and the lamellar interfaces.(a) yield strenth σy and ultimate tensile strength σuts; (b) uniform elongation δuand post-necking elongation, δpn.

    Fig. 5. Fracture surfaces of the macro-tensile specimens tested in the (a, b) RDand (c, d) TD.

    Fig. 6. Overall fracture morphologies of the micro-spec

    Z. You et al. Nano Materials Science 2 (2020) 72–79

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    only the flow strength and uniform strain but also the non-uniformpost-necking ductility can be duplicated in such small specimens. Themicro tension in the TD exhibits only marginally higher (

  • Table 3Calculated flow strengths for the three major texture components in differentstress directions.

    Texture component Flow strength (MPa)

    RD TD ND ID

    Brass f1 1 0g〈1 1 2〉 1454 1789 1789 1332Goss f1 1 0g〈0 0 1〉 1207 1833 1789 1185f1 1 1g〈uvw〉 Fiber 1776 1774 2082 1332

    Fig. 7. Fracture surfaces of the micro-tensile specimens tested in (a) RD, (b) TD,(c) ND, and (d) ID.

    Z. You et al. Nano Materials Science 2 (2020) 72–79

    rotated nearly parallel to the rolling plane [34].To estimate the orientation dependence of the flow strength for the

    severely cold-rolled SS, the anisotropic strengthening effect of theextended planar boundaries should be incorporated into the criticalresolved shear stress (CRSS) [17]:

    τCRSS;i ¼ τ0 þ τd þ kGBd�1=2i (1)

    where τ0 is the friction stress at undeformed state, kGB is the Hall-Petchcoefficient characterizing the strength of grain boundaries (GBs), anddi is the boundary spacing experienced by the ith slip system. The τd termis included to describe the strengthening produced by the dislocationsinside the lamellae. Both τ0 and τd are assumed to be common to all slipsystems; τd is computated as:

    τd ¼ αμbρ1=2 (2)

    where μ (¼ 78 GPa) is the shear modulus of the 316L SS, b (¼ 0.258 nm)is the Burgers vector, α (¼ 0.5) is a material constant, and ρ is the totaldislocation density.

    As schematically illustrated in Fig. 8, the dislocation pile-up length diis calculated as the distance in the slip plane between the lamellarboundaries [17]:

    ψ ¼ arccosðjnLB ⋅ nSPjÞ (3)

    dSP;i ¼ λsin ψ (4)

    where λ is the mean lamellar spacing, and nLB and nSP are unit vectors

    Fig. 8. Schematic illustration of a slip plane intersecting the lamellar bound-aries. nLB and nSP are unit vectors normal to the lamellar boundary and the slipplane, respectively, ψ is the angle between nLB and nSP, λ is the lamellarthickness, and di is the dislocation pile-up length (assumed to be the distance inthe slip plane between the lamellar boundaries).

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    normal to the lamellar boundary and to the slip plane, respectively.By incorporating Eq. (1) into the conventional Taylor model and

    assuming a uniaxial tensile deformation gradient, the flow strengths forthe major texture components in different stressing directions can becomputed with τ0 ¼ 60 MPa, kGB ¼ 1160 MPa nm1/2, and withρ ¼ 1015 m�2, a dislocation density typical for severely deformed metals.For the {1 1 1} fiber texture associated with the remained nanotwins, theaverage TB spacing (30 nm) is taken as λ in Eq. (3), and the flow strengthis the mean value for all the crystallographic orientations belonging tothe ideal {1 1 1} fiber texture. Table 3 summarizes the calculated results,which should represent the σy values in tension. However, due to theaforementioned strain path effect and evident elastic-plastic transientbehavior, the experimental σy values are significantly reduced in the NDand ID. We therefore compare the modeling results to the σUTS values.The latter should be only slightly larger than the σy values given thediminished strain hardening in extensively deformed metals withoutstrain path effect (as exhibited in the RD). Among the three texturecomponents, the computed flow strengths of the brass texture in the RD,TD and ID are most consistent with the corresponding experimental σUTSvalues in the order of TD > RD > ID. This is in agreement with theobservation that brass is the dominant texture [34], and suggests that theflow stress anisotropy in these directions is principally a consequence ofthe existing texture and the lamellar structures. By contrast, our modelpredicts that the flow strength in the ND should be highest among thetesting directions, unlike the experimental ND σUTS, which is smaller thanthe TD σUTS. This inconsistency is probably related to premature tensilefailure, as discussed below.

    4.4. Orientation dependence of tensile fracture

    The fracture surfaces clearly demonstrate that the tensile directionhas a strong effect on the fracture behavior that is intimately related tothe spatial alignment of the internal lamellar boundaries. The boundariesat the nanometer scale are potential locations of micro-void nucleation[48–50], and the susceptibility of a boundary to void nucleation isenhanced when sharp mechanical variation exists on both sides of theboundary. For the heterogeneous nano-lamellar 316L SS, such discordantboundaries are not hard to find even within the gauge section of themicro specimen, where high strength nanotwin lamellae and elongatedmartensites are possible hard lamellae adjacent to soft austeniticlamellae. If the tensile direction is parallel to the lamellar structure, thehard and soft lamellae are loaded in parallel fashion (i.e., equallystrained), and the stress is locally redistributed (higher stress in the hardregions). Since the strain is compatible, the hard and soft lamellae deformtogether without failure along the boundary, until eventualtrans-lamellar shear rupture.

    However, when the specimen is tensioned normal to the lamellarstructures, the hard and soft lamellae are loaded in serial fashion (i.e.,equally stressed), and the strain is localized and larger in the soft lamellaethan in the hard lamellae. The strain incompatibility which graduallydevelops in the vicinity of the boundary eventually triggers the nucle-ation and growth of micro-void (see Fig. 7c). Considering our experi-mental σUTS, which were smaller than the flow strength we computed forthe ND, the micro-void nucleation and growth likely control the pre-mature necking and thus we could not achieve the full flow strength. For

  • Z. You et al. Nano Materials Science 2 (2020) 72–79

    the case in which tensile direction was highly inclined to the lamellarstructures, the maximum resolved shear stress is on the planar bound-aries, which stimulates concentrated shear parallel to the lamellae. In thisstress condition, the hard lamellae exert little restriction on the contin-uous shear, thus shear cracking eventually occurs along the boundary, asshown in Fig. 7d.

    5. Conclusions

    We investigated the influence of the lamellae orientation on themechanical response of 316L SS with heterogeneous nano-lamellarstructures using micro-scale tensile experiments in directions parallel,normal, and 45� inclined to the nano-lamellae. We showed that the microspecimens produced size independent mechanical properties similar tothose obtainable from macro specimens. The parallel orientation showsthe highest strength and smallest uniform elongation, while the inclinedorientation exhibits the lowest tensile strength. The normal and inclinedorientations exhibit substantially reduced yield strength and pronouncedstrain hardening, which is a consequence of directional back stressdeveloping in the heterogeneous microstructure. The mechanicalanisotropy is well explained given the crystallographic texture andorientation dependent strengthening of the planar boundaries; theexception is the ND, in which the lower strength probably arises frompremature tensile failure.

    Acknowledgments

    The authors acknowledge financial support from the National KeyR&D Program of China (Grant No. 2017YFA0204403). L.L. acknowl-edges financial support by the National Natural Science Foundation ofChina (Grant No. 51931010, 51601196 and U1608257), the LiaoningRevitalization Talents Program (Grant No. XLYC1802026) and the KeyResearch Program of Frontier Science, Chinese Academy of Sciences. S.Q.acknowledges the financial support of the Postgraduate Research &Practice Innovation Program of Jiangsu Province (Grant No.KYCX180408). The authors greatly appreciate the assistance of Jian-sheng Li in the cold rolling process.

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    Revisiting anisotropy in the tensile and fracture behavior of cold-rolled 316L stainless steel with heterogeneous nano-lame ...1. Introduction2. Experimental details3. Results3.1. Microstructure3.2. Tensile properties3.3. Fractographic examination

    4. Discussion4.1. Specimen size effect4.2. Effect of strain path change4.3. Anisotropic flow strength4.4. Orientation dependence of tensile fracture

    5. ConclusionsAcknowledgmentsReferences